If we're going for facts, the facts are these:
1. You are adding a spring. Which direction it works in is irrelevant, spring rate is spring rate.
2. You are not adding any additional, intentional damping force.
So, where, out of those two FACTS as you like to quote, does the idea enter your mind that you're changing the damping?
Done any of that basic math yet? Math is always good for facts, it stops people's brains getting in the way.
*wiki....
In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include Viscous drag in mechanical systems